the philosophy of mathematics oxford readings in philosophy

Download Book The Philosophy Of Mathematics Oxford Readings In Philosophy in PDF format. You can Read Online The Philosophy Of Mathematics Oxford Readings In Philosophy here in PDF, EPUB, Mobi or Docx formats.

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

The author of the highly popular book Think, which Time magazine hailed as "the one book every smart person should read to understand, and even enjoy, the key questions of philosophy," Simon Blackburn is that rara avis--an eminent thinker who is able to explain philosophy to the general reader. Now Blackburn offers a tour de force exploration of what he calls "the most exciting and engaging issue in the whole of philosophy"--the age-old war over truth. The front lines of this war are well defined. On one side are those who believe in plain, unvarnished facts, rock-solid truths that can be found through reason and objectivity--that science leads to truth, for instance. Their opponents mock this idea. They see the dark forces of language, culture, power, gender, class, ideology and desire--all subverting our perceptions of the world, and clouding our judgement with false notions of absolute truth. Beginning with an early skirmish in the war--when Socrates confronted the sophists in ancient Athens--Blackburn offers a penetrating look at the longstanding battle these two groups have waged, examining the philosophical battles fought by Plato, Protagoras, William James, David Hume, Hans-Georg Gadamer, Jacques Derrida, Michel Foucault, Richard Rorty, and many others, with a particularly fascinating look at Nietzsche. Among the questions Blackburn considers are: is science mere opinion, can historians understand another historical period, and indeed can one culture ever truly understand another. Blackburn concludes that both sides have merit, and that neither has exclusive ownership of truth. What is important is that, whichever side we embrace, we should know where we stand and what is to be said for our opponents.

The aim of this series is to bring together important recent writings in major areas of philosophical inquiry, selected from a variety of sources, mostly periodicals, which may not be conveniently available to the university student or the general reader. The editor of each volume contributes an introductory essay on the items appended as a guide to further reading.

The new edition of this highly successful text will once again provide the ideal introduction to free will. This volume brings together some of the most influential contributions to the topic of free will during the past 50 years, as well as some notable recent work.Topics explored in this collection include: the relation between necessity, acting freely, and freedom to act otherwise; different accounts of the capacity for free agency, and the ways in which it can be compromised; grounds for scepticism about free agency and discussions of the relation betweenfree will and responsibility.

Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.

This volume collects a wealth of articles covering a range of topics of practical concern in the field of ethics, including active and passive euthanasia, abortion, organ transplants, capital punishment, the consequences of human actions, slavery, overpopulation, the separate spheres of men and women, animal rights, and game theory and the nuclear arms race. The contributors are Thomas Nagel, David Hume, James Rachels, Judith Jarvis Thomson, Michael Tooley, John Harris, John Stuart Mill, Louis Pascal, Jonathan Glover, Derek Parfit, R.M. Hare, Janet Radcliffe Richards, Peter Singer, and Nicholas Measor.

This volume features a selection of articles concerning ethics and the environment. It offers an introduction to the main debates in the area, and deals with such issues as the duty to future generations, resource conservation, species and wilderness prese